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Promoting some typical spreading dynamics, for instance, the spreading of information, commercial message, vaccination guidance, innovation, and political movement, can bring benefits to all aspects of the socio-economic systems. In this study, we propose a strategy for promoting the spreading of the susceptible-infected-recovered model, which is widely applied to describe these common spreading dynamics in real life. Specifically, we first quantify the potential influence that the addition of each latent edge (that is, edges that do not exist before) could cause to the spreading dynamics. Then, we strategically add the latent edges to the original networks according to the potential influence of each latent edge. Numerical simulations verify the effectiveness of our strategy and demonstrate that our strategy outperforms several static strategies, namely, adding the latent edges between nodes with the largest degree or eigenvector centrality. This study provides an effective way of promoting the spreading of the susceptible-infected-recovered model by modifying the network structure slightly and helps in understanding what a better network structure for the spreading dynamics is. Besides, the theoretical framework established in this study provides inspirations for the further investigations of edge-based promoting strategies for other spreading models.